cache is recreated again every time your function is called, that won't work. Google how memoization is done.

Refactor the function into a recursive Fibonacci function that using a memoized data structure avoids the deficiencies of tree recursion

A simple recursive solution won't work, a recursive solution that uses memoized data will work, and that's what the kata is about.

Your solution doesn't work because it's too slow when called several times in a row, it always calculates all Fibonacci numbers until the nth one.

Recursion don't fit for this kata.
I would to know why my code does not finish while function gives correct results.

Where is the recursion or the memoization? Google to know what those are if you don't know.